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If the polynomial f(x) = x2 + kx - 15, is exactly divisible by x - 5, then the value of k is _______
- a)3
- b)2
- c)-3
- d)-2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, t...
x2 + kx - 15 is exactly divisible by x - 5
Dividing, x2 + kx + 15 by x - 5
We get, 5k + 10 as remainder.
Since, x2 + kx - 15 is exactly divisible by 2x - 5
∴ 5k + 10 = 0
k = -2
Dividing, x2 + kx + 15 by x - 5
We get, 5k + 10 as remainder.
Since, x2 + kx - 15 is exactly divisible by 2x - 5
∴ 5k + 10 = 0
k = -2
Most Upvoted Answer
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, t...
x2 + kx - 15 is exactly divisible by x - 5
Dividing, x2 + kx + 15 by x - 5
We get, 5k + 10 as remainder.
Since, x2 + kx - 15 is exactly divisible by 2x - 5
∴ 5k + 10 = 0
k = -2
Dividing, x2 + kx + 15 by x - 5
We get, 5k + 10 as remainder.
Since, x2 + kx - 15 is exactly divisible by 2x - 5
∴ 5k + 10 = 0
k = -2
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Community Answer
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, t...
To determine the value of k in the polynomial f(x) = x^2 + kx - 15, we need to check if the polynomial is exactly divisible by x - 5.
To check if the polynomial is divisible by x - 5, we can use the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by x - a and the remainder is zero, then f(a) = 0.
So, let's substitute x = 5 into the polynomial and check if the result is zero.
Substituting x = 5 into f(x), we get:
f(5) = (5)^2 + k(5) - 15
= 25 + 5k - 15
= 5k + 10
If the polynomial is exactly divisible by x - 5, then f(5) should be equal to zero.
Setting f(5) = 0, we have:
5k + 10 = 0
Solving for k, we get:
5k = -10
k = -10/5
k = -2
Therefore, the value of k is -2.
Hence, the correct answer is option 'D' (-2).
To check if the polynomial is divisible by x - 5, we can use the remainder theorem. According to the remainder theorem, if a polynomial f(x) is divided by x - a and the remainder is zero, then f(a) = 0.
So, let's substitute x = 5 into the polynomial and check if the result is zero.
Substituting x = 5 into f(x), we get:
f(5) = (5)^2 + k(5) - 15
= 25 + 5k - 15
= 5k + 10
If the polynomial is exactly divisible by x - 5, then f(5) should be equal to zero.
Setting f(5) = 0, we have:
5k + 10 = 0
Solving for k, we get:
5k = -10
k = -10/5
k = -2
Therefore, the value of k is -2.
Hence, the correct answer is option 'D' (-2).
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